Looking on the second screen of Digest::MD5's doc, wherefrom this is derived, I guess the below code is what you want:

#!/usr/bin/perl

use strict;
use warnings;

use Digest::MD5 qw( md5_hex );

my $filename ="compress_logs.pl";

open( FILE, '<', $filename)
    or die "Cannot open file $filename: $!\n";

binmode( FILE );

my $digest1 = Digest::MD5->new->addfile( *FILE )->hexdigest;

print "$digest1  $filename Perl Gen\n";

my $digest2 = `md5sum compress_logs.pl`;
chomp( $digest2 );

print "$digest2 Linux Gen\n";
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